Resonance bond numbers: A graph-theoretic study of bond length variations in silicate crystals

The resonance bond number n, as defined in this paper, is designed to describe the strength of an XO bond as a function of the kinds of atoms present and which atoms are bonded. The calculation of n is made on a fragment extracted from the crystal encompassing the XO bond. If this fragment consists of only the X atom and its coordinating O atoms, then n is numerically equal to the Pauling bond strength, s. In this study a graph-theoretic algorithm is developed permitting the calculation of n using fragments including up to 50 atoms. This algorithm was used to calculate n for all of the bonds in ten silicate crystals. Since bond strength is be inversely related to bond length, we examined the relationship between these two variables and found that n can be used to explain over 70 percent of the variation of XO bond lengths from their average values in the crystals. A fit of the parameter n/r, where r is the row number in the periodic table of the metal atom X, to the observed bond lengths in these crystals yielded the equation R(XO)=1.39(n/r)^?0.22 which explains over 95.5 percent of the variation of bond lengths in the crystals. The fact that the same formula with s replacing n was found in an earlier study to be a good estimator of average bond lengths in crystals shows that n relates to individual variations in bond lengths in crystals in the same way that s relates to average bond lengths in crystals. Using minimum energy SiO, AlO and MgO bond lengths and harmonic force constant data calculated for these bonds in hydroxyacid molecules, theoretical equations similar to those used by Pauling to explain bond length variations in hydrocarbons are derived. Bond lengths calculated with these equations for the 10 crystals shows that 95 percent of the variation of the observed bond lengths in these crystals can be explained in terms of n by this purely theoretical model.     

Power law relationships between bond length, bond strength and electron density distributions

The strength of a bond, defined as p=s/r, where s is the Pauling bond strength and r is the row number of an M cation bonded to an oxide anion, is related to a build-up of electron density along the MO bonds in a relatively large number of oxide and hydroxyacid molecules, three oxide minerals and three molecular crystals. As p increases, the value of the electron density is observed to increase at the bond critical points with the lengths of the bonds shortening and the electronegativities of the M cations bonded to the oxide anion increasing. The assertion that the covalency of a bond is intrinsically connected to its bond strength is supported by the electron density distribution and its bond critical point properties. A connection also exists between the properties of the electron density distributions and the connectivity of the bond strength network formed by the bonded atoms of a structure. Received: 20 August 1997 / Revised, accepted: 3 November 1997     

The crystal chemistry of lithium and Fe3+ in synthetic orthopyroxene

Lithian ferrian enstatite with Li₂O = 1.39 wt% and Fe₂O₃ 7.54 wt% was synthesised in the (MgO–Li₂O–FeO–SiO₂–H₂O) system at P = 0.3 GPa, T = 1,000°C, fO₂ = +2 Pbca, and a = 18.2113(7), b = 8.8172(3), c = 5.2050(2) Å, V = 835.79(9) Å³. The composition of the orthopyroxene was determined combining EMP, LA-ICP-MS and single-crystal XRD analysis, yielding the unit formula ^M2(Mg_0.59Fe _0.21 ²⁺ Li_0.20) ^M1(Mg_0.74Fe _0.20 ³⁺ Fe _0.06 ²⁺ ) Si₂O₆. Structure refinements done on crystals obtained from synthesis runs with variable Mg-content show that the orthopyroxene is virtually constant in composition and hence in structure, whereas coexisting clinopyroxenes occurring both as individual grains or thin rims around the orthopyroxene crystals have variable amounts of Li, Fe³⁺ and Mg contents. Structure refinement shows that Li is ordered at the M2 site and Fe³⁺ is ordered at the M1 site of the orthopyroxene, whereas Mg (and Fe²⁺) distributes over both octahedral sites. The main geometrical variations observed for Li-rich samples are actually due to the presence of Fe³⁺, which affects significantly the geometry of the M1 site; changes in the geometry of the M2 site due to the lower coordination of Li are likely to affect both the degree and the kinetics of the non-convergent Fe²⁺-Mg ordering process in octahedral sites.     

A crystal chemical study of protoanthophyllite: orthoamphiboles with the protoamphibole structure

Two new protoamphibole-type amphiboles with space group type Pnmn, have been found in nature: protoferro-anthophyllite (Fe_0.80Mn_0.20)₂ (Fe_0.98Mg_0.02)₅ (Si₄O₁₁)₂(OH)₂, and protomangano-ferro-anthophyllite, (Mn_0.70Fe_0.30)₂ (Fe_0.82Mg_0.18)₅ (Si₄O₁₁)₂(OH)₂. Protoferro-anthophyllite (PFA) occurs in pegmatites at both Gifu Prefecture, Japan and at Cheyenne Mountain, El Paso County, Colorado, USA. Protomangano-ferro-anthophyllite, (PMFA) occurs in pegmatites at Fukushima Prefecture and in a Mn mine at Tochigi Prefecture, Japan. Structure determinations of the two amphiboles show that both are isostructural with the synthetic fluorian-amphibole, protoamphibole (= protofluorian-lithian-anthophyllite). A calculation of the procrystal electron density distributions, the bond paths and the bond critical point properties of PFA, PMFA, grunerite and protoamphibole indicates that the M4 cation in these amphiboles is 4-coordinated. A calculation of the electron density distributions at the Becke3LYP/6-311G(2d,p) level for model silicate tetrahedra for these amphiboles and anthophyllite reveals that the value of the electron density at the bond critical points, ρ(r _c ), for the SiO(nbr) bonds is larger, on average (0.93 e/ų), than that for the SiO(br) bonds (0.90 e/ų). The observed SiO bond lengths decrease linearly with increasing ρ(r _c ) while the magnitudes of the curvatures of ρ(r _c ) both perpendicular and parallel to the bonds and the Laplacian of ρ(r _c ) each increases. These trends are associated with an increase in the electronegativity of the Si cation, a possible increase in the covalent character of the SiO bond and a tendency for SiO(nbr) bonds to be involved in wider OSiO angles than SiO(br) bonds. It is possible, if not likely, that protoanthophyllite has often been misidentified as anthophyllite.     

A physical basis for Pauling's definition of bond strength

 The average strength, s, of the bonded interactions comprising a cation containing oxide anion coordination polyhedron and the value of the electron density, ρ(r _c ), at the bond-critical points are inversely correlated with bond length. In each case, the observed bond lengths, R, were modeled with power-law expressions defined in terms of s/r and ρ(r _c )/r, respectively, where r is the Periodic Table row number of the cation involved in the bonded interaction. On the basis of the close connection between bond strength and the value of the electron density at the bond-critical point, we conclude that bond strength is a direct measure of bond type; the greater its value, the greater the localization of electron density in the binding region and the greater the shared–electron covalent character of the bonded interaction. Received: 15 October 2002 / Accepted: 17 February 2003 Present address:G. V. Gibbs in care of M. Spackman Department of Chemistry, University of New England, Armidale 2351, Australia Acknowledgements The NSF is thanked for supporting this study with grant EAR–9627458. The paper was written while GVG was a Visiting NSF Scholar at The University of Arizona. The faculty and graduate students of the Department of Geosciences and Bob Downs and Marelina Stimpf in particular are thanked for making the visit great fun.     

The MgCr2O4–MgFe2O4 solid solution series: effects of octahedrally coordinated Fe3+ on T–O bond lengths

The influence on the spinel structure of Fe³⁺ → Cr substitution was studied in flux-grown synthetic single crystals of the magnesiochromite–magnesioferrite (MgCr₂O₄–MgFe₂O₄) solid solution series. Samples were analysed by single-crystal X-ray diffraction, electron microprobe analyses, optical absorption and Mössbauer spectroscopy. With the exception of iron-poor samples (3–12 mol-% MgFe₂O₄), optical absorption and Mössbauer spectra show that iron occurs almost exclusively as trivalent Fe in the present samples. A very intense and broad absorption band at ca 7,800 cm^?1 dominates the optical absorption spectra of samples with higher Fe-contents. The appearance of this band is related to a distinct structural disorder of Fe³⁺ and a development of magnetic ordering as demonstrated by Mössbauer spectra. Profound composition-related changes are observed in the Mössbauer spectra, which are magnetically unsplit in the range 2–41 mol-% magnesioferrite, but become magnetically split in the range 59–100 mol-% magnesioferrite. Structural parameters a ₀ and M–O increase with magnesioferrite content and inversion degree, while u and T–O decrease. Our study confirms the previously reported (Lavina et al. 2002) influence of Fe³⁺ at the M site on T–O bond lengths in the spinel structure.     

A variable-temperature neutron diffraction study of ussingite; a strong asymmetric hydrogen bond in an aluminosilicate framework

A powder neutron diffraction study of ussingite, Na₂AlSi₃O₈(OH), over the temperature range 4–850 K has been undertaken. The strong hydrogen bond that exists in this mineral has been accurately determined with the O–H distance at 1.070(8) Å and an O(donor)–O(acceptor) separation of 2.481(5) Å at 4 K, The distribution of hydrogen along the O–O direction remains asymmetric between 4 and 850 K with the H atom being fully ordered at a single site, rather than partially disordered over two sites of a double-potential well, as in serandite. A gradual increase in the bonded O–H distance at higher temperatures is observed, indicative of a broadening of the potential well in which the hydrogen atom is sited. Below 50 K, the material shows negative thermal expansion, likely to be associated with reduced bending motion of the O–H bond.     

Molecular mimicry of the bond length-bond strength variations in oxide crystals

Minimum energy theoretical bond lengths R _t obtained with robust split-basis molecular orbital calculations for 27 hydroxyacid molecules containing first- and second-row cations X ⁿ⁺ reproduce XO bond lengths in crystals. Plots of ln(R _t ) vs. ln(s), where s is the Pauling bond strength, define two different but essentially parallel trends (for first- and second-row cations, respectively) as observed for crystals. A new bond strength parameter p=s/r is defined where r=1 for first- and r=2 for second-row main-group cations. When a ln(R _t ) vs. ln(p) plot is prepared with these theoretical bond lengths, a single trend is obtained. A regression analysis of this data set shows that more than 99 percent of the variation of ln(R _t can be explained in terms of a linear dependence on ln(p), yielding R=1.39 p ^?0.22 as an estimator of the bond lengths. A comparison of 153 mean XO bond lengths compiled by Shannon (1976) for main-group closed-shell X-cations from all 6 rows of the periodic table with those estimated with this formula for r=1, 2, ..., 6, respectively, shows that these bond lengths are estimated within 0.05 Å on average with nearly 85 percent estimated within 0.10 Å of the observed value. More than 97 percent of the variation of these observed bond lengths can be ranked in terms of a linear dependence on the estimated bond lengths. The success of these calculations is further evidence that the forces that govern bond length variations in oxide crystals behave as if they are short-ranged.     

Single-crystal polarized FTIR spectroscopy and neutron diffraction refinement of cancrinite

We relate a single-crystal FTIR (Fourier transform infrared) and neutron diffraction study of two natural cancrinites. The structural refinements show that the oxygen site of the H₂O molecule lies off the triad axis. The water molecule is almost symmetric and slightly tilted from the (0001) plane. It is involved in bifurcated hydrogen bridges, with Ow···O donor–acceptor distances >2.7 Å. The FTIR spectra show two main absorptions. The first at 3,602 cm^?1 is polarized for E ⊥ c and is assigned to the ν₃ mode. The second, at 3,531 cm^?1, is also polarized for E ⊥ c and is assigned to ν₁ mode. A weak component at 4,108 cm^?1 could possibly indicate the presence of additional OH groups in the structure of cancrinite. Several overlapping bands in the 1,300–1,500 cm^?1 range are strongly polarized for E ⊥ c, and are assigned to the vibrations of the CO₃ group.     

Structural variation of babingtonite depending on cation distribution at the octahedral sites

Babingtonite, Ca₂Fe²⁺Fe³⁺[Si₅O₁₄(OH)] (Z?=?2, space group $ P\overline{1} $ ) from Yakuki mine (Japan), Grönsjöberget (Sweden), Kandivali Quarry (India), Baveno Quarry (Italy), Bråstad Mine (Norway), and Kouragahana (Japan), and manganbabingtonite, Ca₂(Mn²⁺, Fe²⁺)Fe³⁺[Si₅O₁₄(OH)], from Iron Cap mine (USA) were studied using electron-microprobe analysis (EMPA), ⁵⁷Fe Mössbauer analysis and single-crystal X-ray diffraction methods to determine the cation distribution at M1 and M2 and to analyze its effect on the crystal structure of babingtonite. Although all studied babingtonite crystals are relatively homogeneous, chemical zonation due to mainly Fe ? Mn substitution is observed in manganbabingtonite. Mössbauer spectra consist of two doublets with isomer shift (I.S.)?=?1.16–1.22 mm/s and quadrupole splitting (Q.S.)?=?2.33–2.50 mm/s and with I.S.?=?0.38–0.42 mm/s and Q.S.?=?0.82–0.90 mm/s, assigned to Fe²⁺ and Fe³⁺ at the M1 and M2 octahedral sites, respectively. The determined ratio of Fe²⁺/total Fe in manganbabingtonite (0.26) was smaller than that in the others (0.35–0.44) because of high Mn²⁺ content instead of Fe²⁺. The unit-cell parameters of babingtonite are a?=?7.466–7.478, b?=?11.624–11.642, c?=?6.681–6.690 Å, α?=?91.53–91.59, β?=?93.86–93.94, γ?=?104.20–104.34º, and V?=?560.2–562.3 Å³, and those of manganbabingtonite are a?=?7.4967(3), b?=?11.6632(4), c?=?6.7014(2) Å, α?=?91.602(2), β?=?93.989(2), γ?=?104.574(3)º, and V =565.09(5) ų. Structural refinements converged to R ₁ values of 1.64–3.16 %. The <M1-O> distance was lengthened due to the substitution of large octahedral cations such as Mn²⁺ for Fe²⁺. The increase of the M1-O8, M1-O8’ and M1-O13 lengths with mean ionic radii is slightly more pronounced than of the other M1-Oi lengths. The lengthened M1-O13 distance leads the positive correlation between Si5-O15-Si1 angle and M1-O13 distance. The increase of Si2-O3-Si1 and Si5-O12-Si4 angles due to the increase of mean ionic radius of M2 is also observed.     

Quantification of groundwater–seawater interaction in a coastal sandy aquifer system: a study from Panama,Sri Lanka

The Panama coastal aquifer system is an important water resource in the southeast coast of Sri Lanka that provides adequate supplies of water for agriculture and domestic uses. One of the biggest threats to these fragile aquifers is the sea water intrusion. In this study, recharging mechanism and geochemical evaluation of groundwater in the coastal sandy aquifer of Panama were evaluated using chemical and stable isotope techniques. Thirty groundwater samples were collected and analyzed for their major ion concentrations and stable isotope ratios of oxygen (¹⁸O/¹⁶O) and hydrogen (D/H). All studied samples showed a ranking of major anions in the order Cl^? > HCO ₃ ^?  > SO ₄ ^2?  > N-NO₃ ^? while cations showed a decreasing order of abundance with Na⁺ > Ca²⁺ > Mg²⁺ > K⁺. Dominant groundwater hydrogeochemical types were Na–Cl and mixed Ca–Mg–Cl. Results of saturation index calculations indicate that the investigated groundwater body was mostly saturated with respect to calcite, dolomite and gypsum. In addition, stable isotope and geochemical data suggest that fresh groundwater in the aquifer is recharged mainly by local precipitation with slight modification from evaporation and saline water intrusions. Isotope data suggest that mixing of salt water with freshwater occurs in aquifers which are located towards the lagoon. Since the communities in the study area depend entirely on groundwater, an understanding of the hydrogeochemical characteristics of the aquifer system is extremely important for the better water resource management in the region.     

Effects of temperature on the crystal structure of epidote: a neutron single-crystal diffraction study at 293 and 1,070 K

The effects of temperature on the crystal structure of a natural epidote [Ca_1.925 Fe_0.745Al_2.265Ti_0.004Si_3.037O₁₂(OH), a = 8.890(6), b = 5.630(4), c = 10.150(6) Å and β = 115.36(5)°, Sp. Gr. P2₁ /m] have been investigated by means of neutron single-crystal diffraction at 293 and 1,070 K. At room conditions, the structural refinement confirms the presence of Fe³⁺ at the M₃ site [%Fe(M3) = 73.1(8)%] and all attempts to refine the amount of Fe at the M(1) site were unsuccessful. Only one independent proton site was located. Two possible hydrogen bonds, with O(2) and O(4) as acceptors [i.e. O(10)–H(1)···O(2) and O(10)–H(1)···O(4)], occur. However, the topological configuration of the bonds suggests that the O(10)–H(1)···O(4) is energetically more favourable, as H(1)···O(4) = 1.9731(28) Å, O(10)···O(4) = 2.9318(22) Å and O(10)–H(1)···O4 = 166.7(2)°, whereas H(1)···O(2) = 2.5921(23) Å, O(10)···O(2) = 2.8221(17) Å and O(10)–H(1)···O2 = 93.3(1)°. The O(10)–H(1) bond distance corrected for “riding motion” is 0.9943 Å. The diffraction data at 1,070 K show that epidote is stable within the T-range investigated, and that its crystallinity is maintained. A positive thermal expansion is observed along all the three crystallographic axes. At 1,070 K the structural refinement again shows that Fe³⁺ share the M(3) site along with Al³⁺ [%Fe(M3)_1,070K = 74(2)%]. The refined amount of Fe³⁺ at the M(1) is not significant [%Fe(M1)_1,070K = 1(2)%]. The tetrahedral and octahedral bond distances and angles show a slight distortion of the polyhedra at high-T, but a significant increase of the bond distances compared to those at room temperature is observed, especially for bond distances corrected for “rigid body motions”. The high-T conditions also affect the inter-polyhedral configurations: the bridging angle Si(2)–O(9)–Si(1) of the Si₂O₇ group increases significantly with T. The high-T structure refinement shows that no dehydration effect occurs at least within the T-range investigated. The configuration of the H-bonding is basically maintained with temperature. However, the hydrogen bond strength changes at 1,070 K, as the O(10)···O(4) and H(1)···O(4) distances are slightly longer than those at 293 K. The anisotropic displacement parameters of the proton site are significantly larger than those at room condition. Reasons for the thermal stability of epidote up to 1,070 K observed in this study, the absence of dehydration and/or non-convergent ordering of Al and Fe³⁺ between different octahedral sites and/or convergent ordering on M(3) are discussed.     

Evaluation of hydrogeochemical characteristics of phreatic alluvial aquifers in southeastern coastal belt of Prakasam district, South India

The assessment of hydrogeochemical processes that govern the water quality of inland freshwater aquifers in coastal environment, especially in Indian sub-continent, is occasionally attempted. To bridge the gap, a detail hydrochemical evaluation of groundwater occurring in coastal alluvium is attempted. Single set of high-density water sampling is done from a limited area to gain an in-depth knowledge of the processes that govern the water chemistry of the sandy aquifers. The water is of weak alkaline nature and less mineralized, EC being < 1,000 μS/cm in many samples. Major ion composition indicates that water is contaminated with excess concentration of nitrates. Ionic abundance is in the order of Cl^? > Na⁺  > Ca²⁺ > HCO₃ ^? > SO₄ ^2? > Mg²⁺  > NO₃ ^?. Na⁺ and Cl^? are almost in similar proportions implying the influence of coastal climate on water quality. The water shows modest variation in their ionic assemblage among different sample points as evident from Schoeller scheme. Groundwater can be classified into three distinct facies viz. Cl^?–Ca²⁺–Mg²⁺, Na⁺–Cl^? and Ca²⁺–Mg²⁺–HCO₃ ^? types. The ionic assemblages, their indices, ratios and cross-plots substantiate that multiple processes were involved in the evolution of the water chemistry. Among them, silicate weathering, halite dissolution, ion exchange and base exchange played prominent role in the ion enrichment of groundwater. The aquatic chemistry is further influenced and modified by marine environment, evapotranspiration and anthropogenic inputs which is authenticated by good correlation (r ² = 1) among the Na⁺–Cl^?, EC–Mg²⁺, Na⁺ and Cl^?. Gibbs plots established that evaporation is more responsible for contribution of minerals to the groundwater than aquifer material. Nitrate contamination can be attributed for poor sewerage disposal mechanism which is aggravated by fertilizer inputs, irrigation practices and agriculture activity. A contrasting correlation (r ² ≥90 to <0.40) among select pairs of ions reassures dissimilar source of those ions, involvement of multiple processes and limited interaction of formation water with aquifer material.     

Critical point properties of electron density distributions for oxide molecules containing first and second row cations

 Minimum energy geometries and electron density distributions, ϱ(r), for ∼40 polyatomic oxide molecules containing first and second row M-cations have been calculated at the Hartree-Fock level with a 6-311++G** basis set. The nature of the bonded interactions in these molecules is examined in terms of the relative electronegativities, χ _M , of the M-cations and the properties of the electron density distribution, ϱ(r _c ), evaluated at the bond critical points, r _c , along each MO bond. As ϱ(r _c ) and the Laplacian of ϱ(r _c ) increase, χ _M increases indicating an increase in the covalent character of the bonded interactions between M and O. The ratios of the curvatures of ϱ(r _c ) indicate that the NO bond is predominantly covalent, that the CO and SO bonds are of intermediate type and that the remaining MO bonds are indicated to be predominantly ionic in character. A comparison of the critical point properties of ϱ(r _c ) and χ _M indicates that the minimum energy MO bond length is an important determinate of the properties of ϱ(r _c ) and the character of the MO bonds. On the other hand, values of the local energy density, H(r _c ), indicate that the LiO, BeO, NaO, MgO and AlO bonds are predominantly ionic and that the BO, CO, NO, SiO, PO and SO bonds are predominantly covalent in character. The χ _M -values provided by the properties of ϱ(r _c ) indicate that the covalent component of a bond increases with decreasing bond length, coordination number and increasing bond strength. Each MO bond seems to represent a unique entity and to possess a distinct set of ϱ(r _c ) properties, the distinction being greater for the more electronegative cations. The bonded radius of the oxide ion, r _b (O), and the χ _M -values determined from ϱ(r _c ) correlate with values determined from promolecule electron density distributions. In addition, r _b (O) and χ _M -values determined from experimental electron density distributions for crystals correlate with values determined from procrystal electron density distributions. The number of critical points and bond paths are modeled rather faithfully by procrystal and promolecule electron density distributions, despite the neglect of the binding forces in their constructions. Received: October 15, 1996/Revised, accepted: February 10, 1997     

Mineralogy, conditions of crystallization and melt generation of epidote-bearing porphyries from the Middle Urals, Russian federation

Epidote-bearing porphyritic dikes (whole rock analysis: SiO₂?=?55–65 wt. %, MgO <2.1 wt. %, K₂O <2.5 wt. %, Al₂O₃ >17 wt. %, Na₂O + K₂O?=?5.7–9.4 wt. %) situated in the continental margin zone, the Middle Urals, Russian Federation have been dated using SHRIMP U-Pb zircon techniques and give a Middle Devonian age of 388?±?2 Ma and 389?±?6 Ma. The porphyries contain phenocrysts of magmatic epidote (Ps?=?17–25 %), Ca- and Mn-rich (CaO >9 wt. %; MnO >6 wt. %) almandine garnet, Al-rich (Al₂O₃?=?12–16 wt. %) amphibole, titanite, plagioclase, biotite, muscovite, apatite, and quartz. 60 to 70 % groundmass of the porphyritic dikes consists of fine-grained albite, quartz, and K-feldspar. A variety of thermobarometric estimations, plus comparison with published experimental data indicate that the phenocryst assemblage was stable between 5 and 11 kbar and 690 to 800 °C. Oxygen fugacity was close to or greater than logfo₂ = Ni-NiO + 1. Later stage formation of the quartz-feldspar groundmass took place at hypabyssal conditions, corresponding to 1 to 2 kbar and 660 to 690 °C. The porphyritic dikes are metaluminous to slightly peraluminous (ACNK?=?0.7–1.17). They are enriched in REE and depleted Nb and Ti. They show features typical of subduction-related magmas. Chemical composition and isotopic ratios of ⁸⁶Sr/⁸⁷Sr_i?=?0.709–0.720 suggest that both mantle- and deep crustal-derived materials were involved in their petrogenesis.     

Antigorite equation of state and anomalous softening at 6 GPa: an in situ single-crystal X-ray diffraction study

The compressibility of antigorite has been determined up to 8.826(8) GPa, for the first time by single crystal X-ray diffraction in a diamond anvil cell, on a specimen from Cerro del Almirez. Fifteen pressure–volume data, up to 5.910(6) GPa, have been fit by a third-order Birch–Murnaghan equation of state, yielding V ₀ = 2,914.07(23) Å³, K _T0 = 62.9(4) GPa, with K′ = 6.1(2). The compression of antigorite is very anisotropic with axial compressibilities in the ratio 1.11:1.00:3.22 along a, b and c, respectively. The new equation of state leads to an estimation of the upper stability limit of antigorite that is intermediate with respect to existing values, and in better agreement with experiments. At pressures in excess of 6 GPa antigorite displays a significant volume softening that may be relevant for very cold subducting slabs.     

Diffusion and solubility of hydrogen and water in periclase

Cylinders of synthetic periclase single crystals were annealed at 0.15–0.5 GPa and 900–1200 °C under water-saturated conditions for 45 min to 72 h. Infrared spectra measured on the quenched products show bands at 3,297 and 3,312 cm^?1 indicating V _OH ^? centers (OH-defect stretching vibrations in a half-compensated cation vacancy) in the MgO structure as a result of proton diffusion into the crystal. For completely equilibrated specimens, the OH-defect concentration, expressed as H₂O equivalent, was calculated to 3.5 wt ppm H₂O at 1,200 °C and 0.5 GPa based on the calibration method of Libowitzky and Rossmann (Am Min 82:1111–1115, 1997). This value was confirmed via Raman spectroscopy, which shows OH-defect-related bands at identical wavenumbers and yields an H₂O equivalent concentration of about 9 wt ppm using the quantification scheme of Thomas et al. (Am Min 93:1550–1557, 2008), revised by Mrosko et al. (Am Mineral 96:1748–1759, 2011). Results of both independent methods give an overall OH-defect concentration range of 3.5–9 (+4.5/?2.6) ppm H₂O. Proton diffusion follows an Arrhenius law with an activation energy E _a = 280 ± 64 kJ mol^?1 and the logarithm of the pre-exponential factor logD_o (m² s^?1) = ?2.4 ± 1.9. IR spectra taken close to the rims of MgO crystals that were exposed to water-saturated conditions at 1,200 °C and 0.5 GPa for 24 h show an additional band at 3,697 cm^?1, which is related to brucite precipitates. This may be explained by diffusion of molecular water into the periclase, and its reaction with the host crystal during quenching. Diffusion of molecular water may be described by logD_H2O (m² s^?1) = ?14.1 ± 0.4 (2σ) at 1,200 °C and 0.5 GPa, which is ~ 2 orders of magnitude slower than proton diffusion at identical P-T conditions.     

Weathering Processes in the Min Jiang: Major Elements, {}^{87}{\text{Sr/}}{}^{86}{\text{Sr}},\;\delta {}^{34}{\text{S}}_{{\text{SO}}_{\text{4}} } ,\;{\text{and}}\;\delta {}^{18}{\text{O}}_{{\text{SO}}_{\text{4}} }

We investigated the dissolved major elements, $ {}^{87}{\text{Sr/}}{}^{86}{\text{Sr}},\;\delta {}^{34}{\text{S}}_{{\text{SO}}_{\text{4}} } ,\;{\text{and}}\;\delta {}^{18}{\text{O}}_{{\text{SO}}_{\text{4}} } $ composition of the Min Jiang, a headwater tributary of the Chang Jiang (Yangtze River). A forward calculation method was applied to quantify the relative contribution to the dissolved load from rain, evaporite, carbonate, and silicate reservoirs. Input from carbonate weathering dominated the major element composition (58–93%) and that from silicate weathering ranged from 2 to 18% in unperturbed Min Jiang watersheds. Most samples were supersaturated with respect to calcite, and the CO₂ partial pressures were similar to or up to ～5 times higher than atmospheric levels. The Sr concentrations in our samples were low (1.3–2.5 μM) with isotopic composition ranging from 0.7108 to 0.7127, suggesting some contribution from felsic silicates. The Si/(Na^* + K) ratios ranged from 0.5 to 2.5, which indicate low to moderate silicate weathering intensity. The $ \delta {}^{34}{\text{S}}_{{\text{SO}}_{\text{4}} } \;{\text{and}}\;\delta {}^{18}{\text{O}}_{{\text{SO}}_{\text{4}} } $ for five select samples showed that the source of dissolved sulfate was combustion of locally consumed coal. The silicate weathering rates were 23–181 × 10³ mol/km²/year, and the CO₂ consumption rates were 31–246 × 10³ mol/km²/year, which are moderate on a global basis. Upon testing various climatic and geomorphic factors for correlation with the CO₂ consumption rate, the best correlation coefficients found were with water temperature (r ² = 0.284, p = 0.009), water discharge (r ² = 0.253, p = 0.014), and relief (r ² = 0.230, p = 0.019).     

Structural investigations,high temperature behavior and phase transition of Na6Ca4(SO4)6F2

Polycrystalline material of a sulfate apatite with chemical composition Na₆Ca₄(SO₄)₆F₂ or (Na₂Ca₄)Na₄(SO₄)₆F₂ has been synthesized by solid state reactions. Basic crystallographic data are as follows: hexagonal symmetry, a?=?9.3976(1) Å, c?=?6.8956(1) Å, V?=?527.39(1) ų, Z?=?1, space group P6₃/m. For structural investigations the Rietveld method was employed. Thermal expansion has been studied between 25 and 600 °C. High temperature (HT) powder diffraction data as well as thermal analysis indicate that the apatite-type compound undergoes a reconstructive phase transition in the range between 610 and 630 °C. Single-crystals of the HT-polymorph were directly grown from the melt. Structural investigations based on single-crystal diffraction data of the quenched crystals performed at ?100 °C showed orthorhombic symmetry (space group Pna2₁) with a?=?12.7560(8) Å, b?=?8.6930(4) Å, c?=?9.8980(5) Å, V?=?1097.57(10) ų and Z?=?2. Unit cell parameters for a quenched polycrystalline sample of the HT-form obtained at ambient conditions from a LeBail-fit are as follows: a?=?12.7875(1) Å, b?=?8.7255(1) Å, c?=?9.9261(1) Å, V?=?1107.53(2) ų. The lattice parameters of both modifications are related by the following approximate relationships: a _HT?≈?2c _RT, b _HT?≈?-(½a _RT?+?b _RT), c _HT?≈?a _RT. The HT-modification is isotypic with the corresponding potassium compound K₆Ca₄(SO₄)₆F₂. The pronounced disorder of the sulphate group even at low temperatures has been studied by maximum entropy calculations. Despite the first-order character of the transformation clusters of sulfate groups surrounding the fluorine anions can be identified in both polymorphs. Each of the three next neighbor SO₄-tetrahedra within a cluster is in turn surrounded by 8–9 M-cations (M: Na,Ca) defining cage-like units. However, in the apatite structure the corresponding three tricapped trigonal prisms are symmetry equivalent. Furthermore, the central fluorine atom of each cluster is coordinated by three next M-neighbors (FM₃-triangles), whereas in the HT-polymorph a four-fold coordination is observed (FM₄-tetrahedra).